How do I make a Blender render look glitchy?
I looked around and found some answers to my problem. This method is for the Blender Internal renderer but it can be changed to work with Cycles very easily.

First, add the original movie/animation/image as a plane. In the plane's material settings set the shading to shadeless. Add a camera to the center of the world and clear its rotation. Move the camera up 5 Blender units. Align the plane in camera view so that it lines up with the camera borders. Add another plane 1 Blender unit above the plane that you are trying to distort. Scale it on the X and Y axis until it also fits the camera bounds (it's okay if it goes over a little bit.)

Visuals:






Go to a separate layer. Add a plane at the center of the world and while in camera view scale it down so that the plane is thin on the Y-axis and long on the X-axis (this depends on what you want but generally it's more believable this way.) Duplicate the plane several times. Every time you duplicate the plane, make sure that you change the size a little bit. Hit A on your keyboard until everything in that layer is selected and press Ctrl+G on your keyboard. After waiting a few seconds, (the more objects you have the longer this will take) everythings outlines should turn green or whatever the grouped color of your Blender theme is.

Visuals:


Next, create the material. Select one of the planes that you just created. In the properties panel go to the material tab. Click the "new" button. Under the shading option set it to shadeless and under transparency set it to raytrace. In the transparency settings set the alpha to 0 and the IOR to 4 (4 isn't necessary, it just gave me the best results.)

Visuals:


Next, go back to the layer with the camera and the video/image that you are trying to glitch. Select the second plane that is above the object that you are glitching and in the properties panel, go to the particle system tab. Create a new particle system. Set the start and end times to the length of the footage and do the same to the length of the animation. Depending on the length of the animation you will have to adjust the emission number value. Set the lifetime to 1 and the random value to .5. Under "physics" set it to "no." Under "render" set it to group and select your group that has the glitch particles. Move the animation 1 frame forward to see the objects. Set the size to a resonable value where the "glitchy" objects are covering a large portion of the image. Uncheck emitter. Check rotation and change the initial oriantation to something that makes your objects appear in the right orientation. For me it was object Y or even global Y. If there aren't enough particles covering your subject matter consider turning the emission number up some.

Visuals:




Now you should be able to configure the output and file format of your project and render it with F12 (for still images) or Ctrl+F12 (for an animation.)

My final result:

www.youtube.com/watch?v=dtl7UeVBkcI

For this render I also used Audacity to remix and distort the music. I did not go over this in my answer.

I hope that this worked for you too! I'll probably add a video tutorial to this later if/when I make it! ;)